Hi there skeptics,

Today I am going to be blogging about a mathematical formula which has had some interest in astronomy in the past, but has since fallen into the waste-bin of science. It has commonly titled as a law, in almost every reference to it and on the Wikipedia page, however, it is best described as an unproven hypothesis, as it has no evidence to support it. The law attempts to represent the approximate distances of the planets from the sun, using the following formula. a = 4 + n, where n = 0, 3, 6, 12, 24, 48, 96 etc., with each new value for n being double the last value. This gives rise to the numbers 4, 7, 10, 16, 28, 52, 100… divide this by 10, 0.4, 0.7, 1, 1.6, 2.8, 5.2, 10… To the 18th century astronomer, this is an astounding set of numbers.

The law was first formulated in 1766 by Johann Titius, who used this simple formula to get these similar numbers. This looked amazing at first, because these numbers fit almost perfectly with the distances in AU (astronomical units) of all the known planets, Mercury through to Saturn. However, there was one number in the sequence that shouldn’t be there, 2.8, no planet was known 2.8 AU from the sun. But sure enough, almost exactly 2.8 AU from the sun, the dwarf planet Ceres was discovered. This was very exiting for astronomers of the time. Could there be a deep, underlying formula to the planets.

They decided to look further, so they started with the next number in sequence, 19.6, and looked from there, and again, triumph, Uranus was discovered by William Herschel in 1781, and you guessed it, it was 19.2 AU from the sun, a mere 2% off the prediction. At this point, astronomers became drunk with enthusiasm, this number sequence is really working well. They went the next step, 38.8, but no, nothing was found. Neptune eventually became the next planet in order, but at 30.1 AU from the sun, it was 29% off, and the law was waning. Next, Pluto, predicted by Titius – Bode to be 77.2 AU away, alack, incorrect, only 39.5 AU from the sun, a 95% inaccuracy.

By this time, the law had fallen into disrepute. No more Titius – Bode being taken seriously by astronomers. Proponents of the law say that these ratios are being found as correct in other star systems around other stars, but these are stars with 1 or 2 planets, meaning that a ratio can always be found, or fit close, due to the set up of the number system. The idea of there being such a simple number which underlies all of the orbits is not one of favour in the astronomical community.

Who knows, there could be a number formula which describes the orbits of planets around a star. There must be, because they all follow the same laws of gravity. But the idea that there is a simple number sequence, not a large, abstract equation with hundreds of influencing factors, is a fringe opinion. Planets could naturally snap into particular grooves around their sun, but no number sequence has stood up to the challenge yet, so science tells us that it probably won’t exist.